This paper investigates the Doppler-bearing tracking problem in the presence of random observer position error at one or two active observers. We first derive the CRLBs for the target and observer location parameters when the noise is Gaussian. The CRLB results indicate that the observer position uncertainty always leads to degradation in the target location estimation accuracy in both the two-observer and single-observer tracking scenarios. In the two-observer case, the Doppler-bearing measurements may be able to improve the observer positions while in the single-observer case, they cannot. This paper then studies the MSE of the target parameter estimate when the observer positions are assumed accurate but in fact have error. We show that for the two-observer case, the MSE is larger than the CRLB of the target parameter vector and thus, it is necessary for an algorithm to take the observer position error into account to achieve the optimum performance. On the other hand, for the single-observer case, the MSE is identical to the CRLB, indicating that the identification of the observer position can be eliminated without sacrificing the estimation accuracy of the target position. Simulations confirm the theoretical results.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.